Question: Solve for $x$ : $ 4|x + 10| + 5 = -3|x + 10| + 2 $
Add $ {3|x + 10|} $ to both sides: $ \begin{eqnarray} 4|x + 10| + 5 &=& -3|x + 10| + 2 \\ \\ { + 3|x + 10|} && { + 3|x + 10|} \\ \\ 7|x + 10| + 5 &=& 2 \end{eqnarray} $ Subtract ${5}$ from both sides: $ \begin{eqnarray} 7|x + 10| + 5 &=& 2 \\ \\ { - 5} &=& { - 5} \\ \\ 7|x + 10| &=& -3 \end{eqnarray} $ Divide both sides by ${7}$ $ \dfrac{7|x + 10|} {{7}} = \dfrac{-3} {{7}} $ Simplify: $ |x + 10| = -\dfrac{3}{7}$ The absolute value cannot be negative. Therefore, there is no solution.